Dense Stars
The agreement of the observational points with the curve is remarkably close, considering the rough nature of the observational measurements; and it seems to afford a rather strong confirmation of the theory. But there is one awful confession to make—we have compared the theory with the wrong stars. At least when the comparison was first made at the beginning of 1924 no one entertained any doubt that they were the wrong stars.
We must recall that the theory was developed for stars in the condition of a perfect gas. In the right half of Fig. 7 the stars represented are all diffuse stars; Capella with a mean density about equal to that of the air in this room may be taken as typical. Material of this tenuity is evidently a true gas, and in so far as these stars agree with the curve the theory is confirmed. But in the left half of the diagram we have the Sun whose material is denser than water, Krueger 60 denser than iron, and many other stars of the density usually associated with solid or liquid matter. What business have they on the curve reserved for a perfect gas? When these stars were put into the diagram it was not with any expectation that they would agree with the curve; in fact, the agreement was most annoying. Something very different was being sought for. The idea was that the theory might perhaps be trusted on its own merits with such confirmation as the diffuse stars had already afforded; then by measuring how far these dense stars fell below the curve we should have definite information as to how great a deviation from a perfect gas occurred at any given density. According to current ideas it was expected that the sun would fall three or four magnitudes below the curve, and the still denser Krueger 60 should be nearly ten magnitudes below.8 You see that the expectation was entirely unfulfilled.
The shock was even greater than I can well indicate to you, because the great drop in brightness when the star is too dense to behave as a true gas was a fundamental tenet in our conception of stellar evolution. On the strength of it the stars had been divided into two groups known as giants and dwarfs, the former being the gaseous stars and the latter the dense stars.
Two alternatives now lie before us. The first is to assume that something must have gone wrong with our theory; that the true curve for gaseous stars is not as we have drawn it, but runs high up on the left of the diagram so that the Sun, Krueger 60, &c., are at the appropriate distances below it. In short, our imaginary critic was right; Nature had hidden something unexpected inside the star and so frustrated our calculations. Well, if this were so, it would be something to have found it out by our investigations.
The other alternative is to consider this question—Is it impossible that a perfect gas should have the density of iron? The answer is rather surprising. There is no earthly reason why a perfect gas should not have a density far exceeding iron. Or it would be more accurate to say, the reason why it should not is earthly and does not apply to the stars.
The sun’s material, in spite of being denser than water, really is a perfect gas. It sounds incredible, but it must be so. The feature of a true gas is that there is plenty of room between the separate particles—a gas contains very little substance and lots of emptiness. Consequently when you squeeze it you do not have to squeeze the substance; you just squeeze out some of the waste space. But if you go on squeezing, there comes a time when you have squeezed out all the empty space; the atoms are then jammed in contact and any further compression means squeezing the substance itself, which is quite a different proposition. So as you approach that density the compressibility characteristic of a gas is lost and the matter is no longer a proper gas. In a liquid the atoms are nearly in contact; that will give you an idea of the density at which the gas loses its characteristic compressibility.
The big terrestrial atoms which begin to jam at a density near that of the liquid state do not exist in the stars. The stellar atoms have been trimmed down by the breaking off of all their outer electrons. The lighter atoms are stripped to the bare nucleus—of quite insignificant size. The heavier atoms retain a few of the closer electrons, but have not much more than a hundredth of the diameter of a fully arrayed atom. Consequently we can go on squeezing ever so much more before these tiny atoms or ions jam in contact. At the density of water or even of platinum there is still any amount of room between the trimmed atoms; and waste space remains to be squeezed out as in a perfect gas.
Our mistake was that in estimating the congestion in the stellar ball-room we had forgotten that crinolines are no longer in fashion.
It was, I suppose, very blind of us not to have foreseen this result, considering how much attention we had been paying to the mutilation of the atoms in other branches of the investigation. By a roundabout route we have reached a conclusion which is really very obvious. And so we conclude that the stars on the left of the diagram are after all not the ‘wrong’ stars. The sun and other dense stars are on the perfect gas curve because their material is perfect gas. Careful investigation has shown that in the small stars on the extreme left of Fig. 7 the electric charges of the atoms and electrons bring about a slight deviation from the ordinary laws of a gas; it has been shown by R. H. Fowler that the effect is to make the gas not imperfect but superperfect—it is more easily compressed than an ordinary gas. You will notice that on the average the stars run a little above the curve on the left of Fig. 7. It is probable that the deviation is genuine and is partly due to superperfection of the gas; we have already seen that imperfection would have brought them below the curve.
Even at the density of platinum there is plenty of waste space, so that in the stars we might go on squeezing stellar matter to a density transcending anything known on the earth. But that’s another story—I will tell it later on.
The general agreement between the observed and predicted brightness of the stars of various masses is the main test of the correctness of our theories of their internal constitution. The incidence of their masses in a range which is especially critical for radiation pressure is also valuable confirmation. It would be an exaggeration to claim that this limited success is a proof that we have reached the truth about the stellar interior. It is not a proof, but it is an encouragement to work farther along the line of thought which we have been pursuing. The tangle is beginning to loosen. The more optimistic may assume that it is now straightened out; the more cautious will make ready for the next knot. The one reason for thinking that the real truth cannot be so very far away is that in the interior of a star, if anywhere, the problem of matter is reduced to its utmost simplicity; and the astronomer is engaged on what is essentially a less ambitious problem than that of the terrestrial physicist to whom matter always appears in the guise of electron systems of the most complex organization.
We have taken the present-day theories of physics and pressed them to their remotest conclusions. There is no dogmatic intention in this; it is the best means we have of testing them and revealing their weaknesses if any.
In ancient days two aviators procured to themselves wings. Daedalus flew safely through the middle air and was duly honoured on his landing. Icarus soared upwards to the sun till the wax melted which bound his wings and his flight ended in fiasco. In weighing their achievements, there is something to be said for Icarus. The classical authorities tell us that he was only ‘doing a stunt’, but I prefer to think of him as the man who brought to light a serious constructional defect in the flying-machines of his day. So, too, in Science. Cautious Daedalus will apply his theories where he feels confident they will safely go; but by his excess of caution their hidden weaknesses remain undiscovered. Icarus will strain his theories to the breaking-point till the weak joints gape. For the mere adventure? Perhaps partly; that is human nature. But if he is destined not yet to reach the sun and solve finally the riddle of its constitution, we may at least hope to learn from his journey some hints to build a better machine.